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Chapter 2: Problem 98

Find the axis of symmetry for each parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is the same as the given point. $$f(x)=3(x+2)^{2}-5 ; \quad(-1,-2)$$

Short Answer

Expert verified
The axis of symmetry for the parabola is \(x = -2\). The second point on the parabola with y-coordinate as -2 is \(-3,-2\).

Step by step solution

01

Recognize the equation and the vertex form

We know that \(f(x)=3(x+2)^{2}-5\) follows the form \(f(x) = a(x-h)^{2} + k\), where (h,k) is the vertex of the parabola. Therefore, h is -2.
02

Find the axis of symmetry

The formula for axis of symmetry is \(x=h\), using the value of h from step 1. This therefore is \(x = -2\).
03

Find a second point with the same y-coordinate

It鈥檚 given that the y-coordinate of a point on the parabola is -2. Knowing this, we set \(f(x) = -2\) and solve for x, getting \(x = -1\) and \(x = -3\). Since the -1 coordinate has been already given, the other coordinate, with x = -3 is the second point required in the problem.

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